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Monday, 12 August 2013

PREPARATION OF QUANTITATIVE SECTION


Syllabus of quant section is very broad. Candidates may classify these broad topics in to sub topics and prepare for each topic one by one.
·         Geometry, (Lines, angles, Triangles, Spheres, Rectangles, Cube, Cone etc)
·         Ratios and Proportion, Ratios,
·          Percentages, In-equations
·         Quadratic and linear equations
·         Algebra
·         Mensuration,
·          Allegation & Mixtures, Work, Pipes and Cisterns
·         Installment Payments, Partnership,
·          Clocks
·         Probability, Permutations & Combinations
·         Profit & Loss
·         Averages, Percentages, Partnership
·         Time-Speed-Distance, Work and time
·         Number system: HCF, LCM,
·         Geometric Progression, Arithmetic progression,
·         Arithmetic mean, Geometric mean , Harmonic mean, Median, Mode,
·          Number Base System,
·          BODMAS, etc.

How to Prepare For Math Topics?
There should be very positive approach for preparation. Try to go through the topic selectively. Clear your concept first then practice. Most Ideal way to prepare is to cover each topics conceptually and go for practice set. For example: You have completed the topics Trigonometry in two days, go for practice set of trigonometry then move to another topic. Try to repeat this for all the topics.
One should not go for multiple books for preparation in any of the Competitive exam. Always try to use one or two books for every subject. One should not prepare for competitive exam after keeping only single exam in mind. 
Practice with NCERT Books 
A Quantitative Aptitude test evaluates you on the numerical ability and accuracy level in the mathematical calculations. It consists of several types of questions ranging from pure numeric calculations to arithmetic reasoning. Also it includes graph and table reading, percentage analysis, categorization, quantitative analysis etc.can be achieved by a lot of practice
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Most scoring topics for any exam should be Arithmetic, Algebra and Number System. The other areas such as Geometry, Mensuration and Higher Math’s .

Hence, you should start the basic preparation with the topics of Arithmetic and Algebra, which are the basic and most scoring parts. The approach to the above mentioned areas will vary from each other, when you are preparing for different exams.

The four areas of Quant viz., Arithmetic, Algebra,and Geometry & Modern Math require different skill sets. 

• Arithmetic: how to 'apply' formulae; 
• Algebra: reading and understanding the question; 
• Geometry; ability to visualize; 
• Modern Math: Your logical reasoning ability.
You understand a piece of mathematics if you can do all of the following:
  • Explain mathematical concepts and facts in terms of simpler concepts and facts.
  • Easily make logical connections between different facts and concepts.
  • Recognize the connection when you encounter something new (inside or outside of mathematics) that's close to the mathematics you understand.
  • Identify the principles in the given piece of mathematics that make everything work. (i.e., you can see past the clutter.)
By contrast, understanding mathematics does not mean to memorize methods, Formulas, Definitions, or Theorems.
Clearly there must be some starting point for explaining concepts in terms of simpler concepts.  For our purposes it suffices to think of elementary school math as the starting point. It is sufficiently rich and intuitive.
All of this is neatly summarized in a letter that Issac newton wrote to Nathaniel Hawes on 25 May 1694.
People wrote differently in those days, obviously the " vulgar mechanick" may be a man and "he that is able to reason nimbly and judiciously" may be a woman, (and either or both may be children).
Mathematical concepts build on simpler mathematical concepts. It's amazing how quickly one can proceed from simple facts to very complicated ones 

Solving Mathematical Problems

The most important thing to realize when solving difficult mathematical problems is that one never solves such a problem on the first attempt. Rather one needs to build a sequence of problems that lead up to the problem of interest, and solve each of them. At each step experience is gained that's necessary or useful for the solution of the next problem. Other only loosely related problems may have to be solved, to generate experience and insight.
Students  often neglect to check their answers. I suspect a major reason is that traditional and widely used teaching methods require the solution of many similar problems, each of which becomes a chore to be gotten over with rather than an exciting learning opportunity. In my opinion, each problem should be different and add a new insight and experience. However, it is amazing just how easy it is to make mistakes. So it is imperative that all answers be checked for plausibility. Just how to do that depends of course on the problem.
The main thing that keeps mathematics alive and interesting of course are unsolved problems. Many open problems that are "important" in the contemporary view are hard just to understand.

Acquiring Mathematical Understanding

Since this is directed to undergraduate students a more specific question is how does one acquire mathematical understanding by taking classes? But that does not mean that classes are the only way to learn something.  What  most people  are interested in and care about, is  solving problems. In particular, when you are no longer a student you will have acquired the skills necessary to learn anything you like by reading and communicating with peers and experts. That's a much more exciting way to learn than taking classes!
Here are some suggestions regarding preparation
  • Always strive for understanding as opposed to memorization.
  • If this means you have to go back, do it! Don't postpone clarifying a point you miss because everything new will build on it.
  • It may be intimidating to be faced with a 1,000 page book and having to spend a day understanding a single page. But that does not mean that you'll have to spend a thousand days understanding the whole book. In understanding that one page you'll gain experience that makes the next page easier, and that process feeds on itself.
  • Do exercises. The teacher may suggest some, put you can pick them on your own from the textbook or make up your own. Select them by the amount of interest they hold for you and the degree of curiosity they stimulate in you. Avoid getting into a mode where you do a large number of exercises that are distinguished only by the numerical values assigned to some parameters.
  • Always check your answers for plausibility.
  • Whenever you do a problem or follow a new mathematical thread explicitly formulate expectations. Your expectations may be met, which causes a nice warm feeling (and you should probably also look for a new and different problem). But otherwise there are two possibilities: you made a mistake from which you can recover, now that you are aware of it, or there is something genuinely new that you can figure out and which will teach you something. If you don't formulate and check expectations you may miss these opportunities.
  • Find a class mate who will work with you in a team. Have one of you explain the material to the other, on a regular basis, or switch periodically. Explaining math to others is one of the best ways of learning it.
  • Be open and alert to the use of new technology. But don't neglect thinking about the problem and understanding it, its solution, and its ramifications. The purposes of technology are not to relieve you of the need to think but:
    • To check your answers.
    • To take care of routine tasks efficiently.
    • To do things that can't possibly be done by hand (like the visualization of large data sets).
Keep in mind a famous maxim: The purpose of computing is insight, not numbers.
  • Once you are done with a course Keep Your Textbook and refer back to it when you need to. You have spent so much time with that book that you know it intimately and know how to use it and where to find the information you need. 
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Always read math problems completely before beginning any calculations.  If you "glance" too quickly at a problem, you may misunderstand what really needs to be done to complete the problem. 
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Whenever possible, draw a diagram.  Even though you may be able to visualize the situation mentally, a hand drawn diagram will allow you to label the picture, to add auxiliary lines, and to view the situation from different perspectives. 
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If you know that your answer to a question is incorrect, and you cannot find your mistake, start over on a clean piece of paper.  Oftentimes when you try to correct a problem, you continually overlook the mistake.  Starting over on a clean piece of paper will let you focus on the question, not on trying to find the error. 
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Do not feel that you must use every number in a problem when doing your calculations. Some mathematics problems have "extra" information.  These questions are testing your ability to recognize the needed information, as well as your mathematical skills. 
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Be sure that you are working in the same units of measure when performing calculations.  If a problem involves inches, feet AND yards, be sure to make the appropriate conversions so that all of your values are in the same unit of measure (for example, change all values to feet). 
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Be sure that your answer "makes sense" (or is logical).  For example, if a question asks you to find the number of feet in a drawing and your answer comes out to be a negative number, know that this answer is incorrect.  (Distance is a positive concept - we cannot measure negative feet.) 
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Remember, that it may be necessary to "solve" for additional information in a problem before being able to arrive at the final answer.  These questions are called "two-step" problems and are testing your ability to recognize what information is needed to arrive at an answer. 
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If time permits, go back and resolve the more difficult problems on the test on a separate piece of paper.  If these "new" answers are the same as your previous answers, chances are good that your solution is correct. 
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Remain confident!  Do not get flustered!  Focus on what you DO know, not on what you do not know.  You know a LOT of math!! 
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When asked to "show work" or "justify your answer", don't be lazy.  Write down EVERYTHING about the problem, Include diagrams, calculations, equations, and explanations written in complete sentences.  Now is the time to "show off" what you really can do with this problem. 
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If you are "stuck" on a particular problem, go on with the rest of the test.  Oftentimes, while solving a new problem, you will get an idea as to how to attack that difficult problem. 
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If you simply cannot determine the answer to a question, make a guess.  Think about the problem and the information you know to be true.  Make a guess that will be logical based upon the conditions of the problem. 
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In certain problems, you may be able to "guess" at an approximate (or reasonable) answer.  After you perform your calculations, see if your final answer is close to your guess. 

Top 10 Preparation Tips for Quantitative Aptitude Test



1. The very first step to prepare well for quantitative aptitude is to know well about the types of questions that are covered under this heading. This can be done by a little bit of research and by taking up the questions of this section.


2. Once you know about the types of questions, one by one take up these types and start preparing.


3. Since this whole section requires a lot of mathematical ability you should revise the basics of mathematics off and on.


4. When you start preparing for a question type take up as many questions as you can from good books and papers and try solving them.


5. Do not consider any type less important or insignificant because you never know which question type may be highlighted in this section.


6. Also, if you are unable to solve a few questions do make it a point to get it solved from a senior, teacher or a fellow student. Don't leave any question unsolved.


7. Quantitative aptitude forms a major section in many significant entrance exams so it shouldn't be taken lightly and must be practiced on a regular basis so that you are in touch with these types of questions.


8 . Once you get in a habit of attempting these questions start focusing on your accuracy. Though it is important to attempt all questions it is equally important to do them accurately.


9. Practice, practice and practice. The more you practice the higher accuracy level you achieve. Only practice can help in a good preparation.


10. After you've worked on achieving a high accuracy level, you need to learn the technique of time management because it is important to attempt the questions correctly in a given amount of time. You cannot just sit for hours solving one question. This again
Quant is an important section in any exam and often the deciding factor, so prepare this section well. The pattern of the exam may be different but the basic preparation will remain same.

For detailed information on particular exams, please go through our earlier blogs  in the months of july and august .

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